Simplify. Express your answer using positive exponents. $\newline$ $\frac{6y^4}{2y^4 \cdot y^8}$

Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

\frac{6y^4}{2y^4 \cdot y^8}

Write Expression, Identify Like Terms: Write down the given expression and identify like terms. $\newline$ The given expression is $\frac{6y^4}{2y^4 \cdot y^8}$ . We can see that $y^4$ appears in both the numerator and the denominator, and we will need to simplify these terms.
Simplify Coefficients and Powers: Simplify the coefficients and the powers of $y$ separately. $\newline$ First, we simplify the coefficients. We have $6$ in the numerator and $2$ in the denominator, which can be simplified as $\frac{6}{2}$ . $\newline$ $\frac{6}{2} = 3$ $\newline$ Next, we simplify the powers of $y$ . We have $y^4$ in the numerator and $y^4 \times y^8$ in the denominator. When dividing powers with the same base, we subtract the exponents. $\newline$ $\frac{y^4}{y^4 \times y^8} = \frac{y^4}{y^{4+8}} = \frac{y^4}{y^{12}}$
Apply Laws of Exponents: Apply the laws of exponents to simplify the powers of $y$ . Using the law of exponents for division, we subtract the exponents of $y$ . $\frac{y^4}{y^{12}} = y^{(4-12)} = y^{-8}$ Since we want to express the answer using positive exponents, we can write $y^{-8}$ as $\frac{1}{y^8}$ .
Combine Coefficients and Powers: Combine the simplified coefficients and powers of $y$ . We have the coefficient $3$ from step $2$ and the power of $y$ as $\frac{1}{y^8}$ from step $3$ . Combining these gives us the final simplified expression. $3 \times \left(\frac{1}{y^8}\right) = \frac{3}{y^8}$